Fourier transform, null variety, and Laplacian's eigenvalues

We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians.

Temperate flowering phenology

Individuals, families, networks, and botanic gardens have made records of flowering times of a wide range of plant species over many years. These data can highlight year to year changes in seasonal events (phenology) and those datasets covering long periods draw interest for their perspective on plant responses to climate change. Temperate flowering phenology is complex, using environmental cues such as temperature and photoperiod to attune flowering to appropriate seasonal conditions. Here we give an overview of flowering phenological recording, outline different patterns of flowering, and look at the interpretation of datasets in relation to seasonal and climatic change.

Synthesis, structure and magnetic properties of mono- and di-nuclear nickel(II) thiocyanate complexes with tridentate N3 donor Schiff bases

The 1:1 condensation of N-methyl-1,3-diaminopropane and N,N-diethyl-1,2-diminoethane with 2-acetylpyridine, respectively at high dilution gives the tridentate mono-condensed Schiff bases N-methyl-N'-(1-pyridin-2-yl-ethylidene)-propane-1,3-diamine (L-1) and N,N-diethyl-N'-(1-pyridin-2-yl-ethylidene)-ethane-1,2-diamine (L-2). The tridentate ligands were allowed to react with methanol solutions of nickel(II) thiocyanate to prepare the complexes [Ni(L-1)(SCN)(2)(OH2) (1) and [{Ni(L-2)(SCN)}(2)] (2). Single crystal X-ray diffraction was used to confirm the structures of the complexes. The nickel(II) in complex 1 is bonded to three nitrogen donor atoms of the ligand L-1 in a mer orientation, together with two thiocyanates bonded through nitrogen and a water molecule, and it is the first Schiff base complex of nickel(II) containing both thiocyanate and coordinated water. The coordinated water initiates a hydrogen bonded 2D network. In complex 2, the nickel ion occupies a slightly distorted octahedral coordination sphere, being bonded to three nitrogen atoms from the ligand L-2, also in a mer orientation, and two thiocyanate anions through nitrogen. In contrast to 1, the sixth coordination site is occupied by a sulfur atom from a thiocyanate anion in an adjacent molecule, thus creating a centrosymmetric dimer. A variable temperature magnetic study of complex 2 indicates the simultaneous presence of zero-field splitting, weak intramolecular ferromagnetic coupling and intermolecular antiferromagnetic interactions between the nickel(II) centers.

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

Modelling of surface identifying characteristics using Fourier series

Texture and small-scale surface details are widely recognised as playing an important role in the haptic identification of objects. In order to simulate realistic textures in haptic virtual environments, it has become increasingly necessary to identify a robust technique for modelling of surface profiles. This paper describes a method whereby Fourier series spectral analysis is employed in order to describe the measured surface profiles of several characteristic surfaces. The results presented suggest that a bandlimited Fourier series can be used to provide a realistic approximation to surface amplitude profiles.

Assessment of the consistency of H2O line intensities over the near-infrared using sun-pointing ground-based Fourier transform spectroscopy

We report on the consistency of water vapour line intensities in selected spectral regions between 800–12,000 cm−1 under atmospheric conditions using sun-pointing Fourier transform infrared spectroscopy. Measurements were made across a number of days at both a low and high altitude field site, sampling a relatively moist and relatively dry atmosphere. Our data suggests that across most of the 800–12,000 cm−1 spectral region water vapour line intensities in recent spectral line databases are generally consistent with what was observed. However, we find that HITRAN-2008 water vapour line intensities are systematically lower by up to 20% in the 8000–9200 cm−1 spectral interval relative to other spectral regions. This discrepancy is essentially removed when two new linelists (UCL08, a compilation of linelists and ab-initio calculations, and one based on recent laboratory measurements by Oudot et al. (2010) [10] in the 8000–9200 cm−1 spectral region) are used. This strongly suggests that the H2O line strengths in the HITRAN-2008 database are indeed underestimated in this spectral region and in need of revision. The calculated global-mean clear-sky absorption of solar radiation is increased by about 0.3 W m−2 when using either the UCL08 or Oudot line parameters in the 8000–9200 cm−1 region, instead of HITRAN-2008. We also found that the effect of isotopic fractionation of HDO is evident in the 2500–2900 cm−1 region in the observations.